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hyreg2: An R package to Estimate Latent Classes on a Mixture of Continuous and Dichotomous Data

The paper introduces **hyreg2**, an R package that provides a user-friendly frequentist framework for estimating latent class models on mixed continuous and dichotomous data using a joint likelihood approach and the EM algorithm, while accommodating heteroskedasticity and censored data.

Original authors: Svenja Elkenkamp, John Grosser, Kim Rand

Published 2026-06-16

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Svenja Elkenkamp, John Grosser, Kim Rand

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to understand a complex group of people, but you only have two different kinds of clues about them:

A "Yes/No" clue: Did they buy a product? (Dichotomous data)
A "How Much" clue: How much money were they willing to spend? (Continuous data)

Usually, statisticians look at these clues separately. They might run one analysis to see who buys things and another to see how much they spend. But the authors of this paper argue that these two clues are actually two sides of the same coin. They come from the same underlying decision-making process.

The paper introduces a new tool called hyreg2 (a package for the R programming language) that lets you look at both clues at the same time to get a clearer picture.

Here is the breakdown of what the paper claims, using simple analogies:

1. The "Hybrid" Detective (The Core Idea)

Think of the data as a mystery. You have suspects (people) who give you two types of testimony: a simple "Yes/No" and a detailed number.

The Old Way: You ask one detective to analyze the "Yes/No" answers and a different detective to analyze the numbers. They work in separate rooms and never compare notes.
The hyreg2 Way: You hire one "Hybrid Detective" who looks at both the "Yes/No" and the numbers simultaneously. The paper claims this detective is smarter because they can see how the two clues influence each other, leading to a more accurate story about what is really happening.

2. Finding Hidden Groups (Latent Classes)

Sometimes, the group of people you are studying isn't just one big blob. They might actually be two or more distinct sub-groups with different habits, even if you can't see the groups with your eyes.

The Analogy: Imagine a room full of people eating pizza. Some people eat the crust, some don't. Some like pepperoni, some don't. If you just look at the whole room, you might think everyone is the same.
What hyreg2 does: It uses a mathematical "flashlight" (called the Expectation-Maximization algorithm) to shine a light on the data and reveal hidden sub-groups. It might find that "Group A" loves pepperoni and eats the crust, while "Group B" hates pepperoni and throws the crust away.
The Paper's Claim: The paper says that if you ignore these hidden groups, your results will be "blurry" or biased. hyreg2 helps you separate the groups so you can understand each one clearly.

3. The "Magic Recipe" (How it Works)

The paper explains that this tool is built on a "recipe" (a mathematical model) that was already invented by other researchers (Ramos-Goñi et al.).

The Problem: Before this paper, using this recipe was like trying to bake a cake without a cookbook. You had to be a master chef (a highly skilled programmer) to write the code yourself. If you weren't an expert, you couldn't use it.
The Solution: The authors built a user-friendly kitchen (the hyreg2 package). They took that complex recipe and put it into a box with a simple dial. Now, anyone can turn the dial, put in their data, and get the cake (the results) without needing to know how to bake from scratch.

4. Special Features (What Else It Can Do)

The paper highlights a few special tools included in this package:

Handling "Censored" Data: Sometimes data is cut off. For example, if a survey asks "How much would you pay?" and the answer is capped at $100, the tool knows how to handle that limit without getting confused.
Uneven Variance (Heteroskedasticity): Sometimes, the "Yes/No" answers are very consistent, but the "How much" answers vary wildly. The tool can adjust for this unevenness, like a camera that auto-focuses on both a still object and a moving one.
Non-Linear Formulas: It can handle complex, curved relationships, not just straight lines.

5. The Real-World Test (The Case Study)

To prove it works, the authors tested it on health data (specifically the EQ-5D-5L questionnaire).

The Context: This questionnaire asks people about their health. Some questions are "Yes/No" (Do you have pain?), and others are "How much" (How much would you trade to be healthy?).
The Result: They used the tool to find hidden groups of people with different health preferences. They showed that the tool produces results that match existing, trusted software (called xreg) when looking at a single group, but goes further by successfully splitting the data into two distinct groups with different preferences.

Summary

The paper claims that hyreg2 is a new, easy-to-use tool that allows researchers to:

Mix "Yes/No" and "Number" data together in one analysis.
Automatically find hidden sub-groups within that data.
Do all this without needing to be a coding expert.

It is designed to make a complex statistical method accessible to everyone, ensuring that when we study mixed data (like in health, economics, or marketing), we don't miss the hidden patterns that separate different types of people.

Technical Summary of "hyreg2: An R package to Estimate Latent Classes on a Mixture of Continuous and Dichotomous Data"

Problem Statement
Statistical research across disciplines such as health economics, marketing, and clinical trials frequently requires the joint modeling of mixed outcome types—specifically continuous and dichotomous data—under the assumption that they arise from a common underlying data-generating process. While hybrid models (joint likelihood models) offer more efficient estimation and coherent parameter interpretation compared to separate analyses, existing software solutions present significant barriers. Bayesian frameworks (e.g., brms, MCMCglmm) are flexible but require complex prior specification, which can be challenging in contexts like first-time clinical evaluations. Conversely, frequentist maximum likelihood approaches are often limited: tools like lme4 handle different distributions but lack joint likelihood capabilities across data types, while flexible frameworks like TMB require users to explicitly program complex likelihood functions. Furthermore, existing implementations of the specific hybrid model proposed by Ramos-Goñi et al. [2017] (e.g., xreg in R, hyreg in Stata) do not support the estimation of latent class models, preventing the identification of unobserved heterogeneity within the population.

Methodology
The paper introduces a frequentist framework for estimating latent class models on a mixture of continuous and dichotomous data. The core methodological approach combines:

Joint Likelihood Formulation: The model assumes continuous responses follow a normal distribution and dichotomous responses follow a binomial distribution. These are linked via a shared set of model parameters and a scaling parameter $\theta$ (where $\beta_{continuous} = \theta \times \beta_{dichotomous}$ ). The joint log-likelihood is maximized, assuming conditional independence between the two outcome types given the latent class.
Latent Class Analysis (LCA): The population is modeled as a finite mixture of $K$ latent subgroups, each characterized by distinct parameters ( $\beta_k, \sigma_k, \theta_k$ ).
Expectation-Maximization (EM) Algorithm: Estimation is performed using the EM algorithm, implemented via the flexmix package.
- E-step: Calculates posterior class probabilities for each observation.
- M-step: Maximizes the weighted log-likelihood for each class. This step utilizes a custom driver (FLXMRhyreg) that defines the joint likelihood and employs bbmle::mle2 for parameter optimization.
Extensions: The framework supports heteroscedasticity (via a separate variance model for continuous data), censored data (using bounded optimization), and non-linear model specifications (via "non-classic" formulas where parameters are explicitly defined rather than inferred from column names).

Key Contributions: The hyreg2 Package
The primary contribution is the hyreg2 R package, which provides a user-friendly implementation of the Ramos-Goñi et al. [2017] model extended to latent class analysis. Key features include:

Accessibility: Users can estimate complex joint likelihood latent class models without programming the likelihood function or the EM algorithm manually.
Flexibility: The package supports homoscedastic (hyreg2) and heteroscedastic (hyreg2_het) error structures, censored data, and non-linear formulas.
Partial Coefficients: It allows for the specification of variables that affect only the continuous or only the dichotomous part of the model.
Visualization and Diagnostics: Dedicated functions (summary_hyreg2, plot_hyreg2) facilitate result interpretation and class assignment visualization.
Compatibility: When $k=1$ (no latent classes), the package reproduces results equivalent to the xreg package, ensuring consistency with established literature.

Results and Validation
The paper validates the package through two main avenues:

Reproducibility: In a case study using EQ-5D-5L valuation data, the hyreg2 estimates for a single-component model ( $k=1$ ) matched those from the xreg package up to the third decimal place, confirming the correct implementation of the underlying joint likelihood framework.
Latent Class Detection: The package successfully identified two latent classes in the EQ-5D data. Visualization revealed distinct preference patterns: Class 2 participants tended to reject health states (assigning higher utility values) more frequently and at lower levels of impairment compared to Class 1. This demonstrates the package's ability to detect preference heterogeneity that would be masked in aggregated models.
Advanced Features: The paper demonstrates successful estimation of models with censored data (bounded TTO values), heteroscedasticity (variance modeled as a function of covariates), and non-classic formulas (e.g., the 8-parameter EQ-5D model and non-linear transformations).

Significance and Claims
The authors position hyreg2 as a bridge between advanced statistical methodology and practical application. The significance of the work lies in lowering the barrier to entry for applying latent class joint likelihood models, particularly for researchers who are not expert programmers. By offering a frequentist alternative to Bayesian approaches, the package addresses the difficulty of specifying priors in novel clinical or economic settings. The authors modestly claim that while the model was motivated by health economics (EQ-5D value sets), its structure is generic and applicable to any domain involving jointly observed continuous and dichotomous data, such as consumer behavior (purchase incidence vs. willingness-to-pay) or clinical trials (toxicity vs. efficacy). The paper concludes that hyreg2 produces plausible and meaningful results but notes that, like all maximum likelihood estimations, results can be sensitive to starting values, recommending the use of bootstrapping or multiple starting points to ensure global convergence. Future development directions identified by the authors include extending non-classic formula support to the heteroscedastic function and implementing automated model selection.